Problem: Simplify the expression. $(-q+8)(3q+5)$
First distribute the ${-q+8}$ onto the ${3q}$ and ${5}$ $ = {3q}({-q+8}) + {5}({-q+8})$ Then distribute the ${3q}.$ $ = ({3q} \times {-q}) + ({3q} \times {8}) + {5}({-q+8})$ $ = -3q^{2} + 24q + {5}({-q+8})$ Then distribute the ${5}$ $ = -3q^{2} + 24q + ({5} \times {-q}) + ({5} \times {8})$ $ = -3q^{2} + 24q - 5q + 40$ Finally, combine the $x$ terms. $ = -3q^{2} + 19q + 40$